SMITHSONIAN MISCELLANEOUS COLLECTIONSVOLUME 82 NUMBER 7
THE ATMOSPHERE AND THE SUN
BYH. HELM CLAYTON
(Publication 3062)
CITY OF WASHINGTONPUBLISHED BY THE SMITHSONIAN INSTITUTIONJUNE 9. 1930

SMITHSONIAN MISCELLANEOUS COLLECTIONSVOLUME 82, NUMBER 7
THE ATMOSPHERE AND THE SUN
BYH. HELM CLAYTON
&
(Publication 3062)
CITY OF WASHINGTONPUBLISHED BY THE SMITHSONIAN INSTITUTIONJUNE 9, 1930
£#e Boti> Qk>afttmore (fitteeBALTIMORE, MD., U. S. A.
THE ATMOSPHERE AND THE SUNBy H. HELM CLAYTONCONTENTS PAGEIntroduction II. Solar changes iII. Latitude effect of solar changes on the earth's atmosphere 4III. Seasonal influences 14IV. Atmospheric waves 18V. Relation of the weather waves to solar changes 29VI. Solar cycles and weather cycles 32VII. The use of weather cycles in forecasting 44Summary 48INTRODUCTIONThis paper is the fifth of a series giving the results of investiga-tions of the relation of solar activity to atmospheric changes. Theearlier ones were published as Smithsonian Miscellaneous Collec-tions, Vol. 68, No. 3; Vol. 71, No. 3; Vol. 77, No. 6; and Vol. 78,No. 4. The author has been stimulated to continue these researchesbecause he believes in their great importance. The interest ofDr. C. G. Abbot and the sympathy and aid of Mr. John A. Roeblinghave encouraged him in the task and enabled him to undertake muchwork that otherwise would not have been possible. Miss M. I. Rob-inson has aided in the calculations needed for the discussion.
I. SOLAR CHANGES
It has long been known that spots appear on the surface of thesun and that the number and size of these spots varies from dayto day, from month to month, and from year to year. More recentlyit has been discovered by Dr. C. G. Abbot and his associates that theradiation coming from the sun varies ; so that, in general, it is knownthat the sun is hotter when there are many spots on its surface thanwhen there are few or none.There is also evidence that the heat of the sun varies from dayto day and from week to week in short cycles of change. The mostconvincing evidence of this fact is the comparison of measurementsSmithsonian Miscellaneous Collections, Vol. 82, No. 7
2 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 82
of solar radiation made at observatories thousands of miles distantfrom each other, one in the northern hemisphere and the other inthe southern hemisphere ; so that the chance of both being affectedby the same weather changes becomes very small. The solar radia-tion reaching the earth is measured in calories per square centimeterper minute, and averages about 1.940 calories. Table 1 shows a com-parison of observations of solar radiation made simultaneously innorthern Chile and in the United States (first in California and thenin Arizona) during the years 1918 to 1924. The table shows thefrequency of different values observed in the United States for eachincrease of .010 calorie in Chile.
Table i.—Comparison of Solar Radiation Values in Chile and the United States{Number of Cases )Values in Values observed in ChileUnited , A 1States 1. 910-9 1.920-9 1.930-9 1-940-9 1-950-9 1.960-9I.89O-9 6661.900-9 II II I OOO1.910-9 20 25 11 5 4 o1.920-9 18 38 21 5 4 21.930-9 7 23 29 11 111.940-9 4 6 12 15 16 41.950-9 4 10 10 13 61.960-9 1 3 4 7 51.970-9 0* 1 1 3 2
If there were no relation between the measurements at the twostations, the observed values would be scattered through the dif-ferent classes at random. The tabulation shows that a random dis-tribution does not exist ; but for each group of observations in Chile,there is a maximum near the same values in the observations in theUnited States. There is, therefore, a progressive displacement ofthe maximum frequency as the solar values increase from 1.910-9to 1 .960-9, or nearly three per cent of the mean value. The probableerror of the measurements is ± .006 calorie ; so that the solar varia-tion during the interval covered by the observations was more thaneight times the probable error of each group of observed values.Since variability in solar radiation has been questioned by someinvestigators, it is well to state that the evidence of this variabilityrests on three fundamental and independent facts
:
( 1 ) The changes in radiation are alike when measured at twowidely separated stations, allowing for variations from a middlevalue due to errors of observation.
NO. THE ATMOSPHERE AND THE SUN CLAYTON(2) The changes both of short period and of long period in solarradiation are related to visible changes in the number and area ofspots, faculae and flocculi seen on the sun.(3) The changes in solar radiation are correlated with other phe-nomena such as certain changes in terrestrial magnetism, in radio-receptivity, and meteorological changes which are known by otherevidence to be related to solar conditions.The critics of solar variability have pointed out that the measuredvariations have decreased as the accuracy of the observations in-creased and that in the earlier observations the effects of water vaporDAYS BEFOREG 4 2 DAYS AFTER1.952
1.951 11.9501.949 f/1.9481.947 i1.946 1
» f ? 2 4 6 8 10 12 14 16 18 20
I 1 |Ceriterf ill I I I s\ Iof sun
Fig. 1.—Calcium flocculi and solar radiation. The mean values of solarradiation received at the earth in calories per square centimeter per minute ondays before and days after the passage of calcium flocculi across the centralmeridian of the sun. 1918-1920. Flocculi of 400 or more on the Ebro scale ofvalues.in the air, of dust, of ozone, and of turbidity were not entirelyeliminated ; but they have in no manner destroyed or impaired thesefundamental evidences of variability.Abbot and his associates ' have given evidence of the relation ofsolar radiation changes to solar contrast and to groups of spots onthe sun, Fowle ' has shown a relation to groups of flocculi, and 1 3have shown a relation to faculae. Bauer 4 has shown a relation to cer-tain changes in terrestrial magnetism, and Austin a has found a
1 Smithsonian Misc. Coll., Vol. 66, No. 5, 1916.2 Idem, Vol. 77, No. 5, 1925.
:; Idem, Vol. 77, No. 6, p. 53, 1925.4 Terr. Mag., Vol. 20, pp. 143-158, Dec, 1915.5 Smithsonian Misc. Coll., Vol. 80, No. 2, p. 13, 1927.
4 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 82
marked parallelism between radio-receptivity and changes in monthlyvalues of solar radiation.In order to study further the relation of clouds of calcium andhydrogen as seen in faculae and flocculi to solar radiation I tookfrom the publication of the Ebro Observatory all days on whichthe area of observed clouds of flocculi exceeded 400 millionths onthe Ebro scale. The day on which this area crossed the centralmeridian of the sun as seen from the earth was called zero day.Then, the solar radiation measured on that day and on each of theseven days preceding was averaged. The same was done for eachof the following days up to 21 days later. The mean values for eachday are shown plotted in figure 1. This plot shows that the radia-tion from the sun averaged lowest when the flocculi were near thecenter of the sun. This fact indicates changes of transparency inthe sun's atmosphere and is interpreted to mean that the clouds ofcalcium and hydrogen in the flocculi cut off the radiation from thesurface of the sun, just as water-vapor clouds cut off radiation fromthe surface of the earth beneath them. When near the limb of thesun, however, these clouds add to the total radiation.
II. LATITUDE EFFECT OF SOLAR CHANGES ON THE EARTH'SATMOSPHEREStudies of the relation of solar radiation changes to meteorologicalchanges have been published in four preceding papers in this series.The results of recent researches and deductions drawn from thewhole mass of data follow. Some readers may be inclined to thinkthat the generalizations given are based on too small an amount ofdata, but in reality they are based on a large amount of data accumu-lated during 20 years of research. Where one example is given, manyothers might have been presented.In the earlier papers of this series the first finding of importancewas that there was a marked latitude effect of solar radiation changeson the pressure and temperature of the earth's atmosphere. Accom-panying or immediately following short-period changes in radiation,there was an increase in temperature and a fall of pressure in equa-torial regions, a rise of pressure and a fall of temperature between40 and 60 ° latitude, while at latitudes above yo° the pressure felland the temperature rose. These conditions hold true for both thenorthern and southern hemispheres. The chart illustrating this factis reproduced in figure 2.Figure 3 shows how, in the average of many cases, day to daychanges of pressure at Honolulu are associated with simultaneous
no. 7 THE ATMOSPHERE AND THE SUN CLAYTON
changes of pressure at Nome and also with day to day changes insolar radiation. During the interval covered bv the data from which
Fig. 2.—Zonal effect of increased solar activity. Shaded areas show regionswhere the pressure falls and the temperature rises with short period changes ofsolar radiation. Unshaded areas show regions where the reverse conditions occur.these curves were constructed, January to April, 1928, the pressureat Nome followed the solar radiation changes directly, and the pres-sure at Honolulu followed inversely. The changes are nearly simul-DAY5 BEFORE DAYS AFTER
30.10
30.05
30.00
29.80
29.75
1.945
.940
Fig. 3.—Maxima of pressure at Honolulu compared with pressureat Nome and with solar radiation.taneous except that the solar minimum and maximum appear tooccur slightly earlier.
6 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 82A later investigation disclosed that there were also latitude dif-ferences in pressure correlated with changes in the monthly num-ber of sun spots. 1 Using the data from about 200 stations, the aver-age pressure when sun spots were near their maximum frequencywas compared with the average pressure in the same latitudes whenthe sun spots were near a minimum of frequency and differencesobtained. These differences are plotted in figure 4.Figure 4, shows that when sun spots are more frequent in num-ber, the pressure is lower in the equatorial region from about 30°N.to 30°S., while from about latitude 35 to 65 in both hemispheres,the pressure is higher when the sun spots are most numerous. Thisresult is in good agreement with that found for short period changes
NO. 7 THE ATMOSPHERE AND THE SUN CLAYTON J
no values of solar radiation were available, only sun-spot numberswere used and an equivalent value of solar radiation was derivedfrom Abbot's ' plots of equivalent values and placed in parentheses.Since both sun-spot numbers and increased "solar radiation areconsidered in forming this table, the results derived from a compari-son of the data in the table with meteorological conditions rest onTable 2.—Relative Sun-spot Numbers and Average Values of Solar RadiationUsed in StudyHigh solar values Low solar valuesDate Sun-spot Solar Date Sun-spot Solarsummer number radiation summer number radiationApr. 1916 72 (1.952) Apr. 1912 4 (1.928)
" 1918 81 1.953 '• 1913 I (1.925)May 1917 114 1.956 May 1910 22 1.9161920 34 1-953 " 1913 o (1.923)June 1905 49 1.968 June 1909 23 1.9301919 hi 1-955 " 1912 4 1.930July 1906 103 1.962 July 1910 14 1.913
*' 191/ 120 1.989 " 1911 3 1.917Aug. 1917 154 1.956 Aug. 1909 23 1.926
" 1918 102 1.954 " 1910 11 1.912Sept. 1917 129 1.948 Sept. 1909 39 1.908I9 J 8 80 1.944 " 1910 26 1.915Mean 95.7 1.958 Mean 8.3 1.917Winter WinterOct. 1917 72 1.952 Oct. 191
1
3 1.915
" 1918 85 1.939 " 1913 3 1.866Nov. 1917 96 (i.954) NTov. 1911 4 1.903
" 1919 42 (i.953) " 1913 1 1.866Dec. 1917 129 (i.957) Dec. 191 2 (1.926)1920 40 1.955 " 1913 4 (1.928)Jan. 1918 96 (1.954) Jan. 1911 3 (1.927)1920 59 1.964 " 1913 2 (1.925)Feb. 1918 65 (1.95O Feb. 1912 o (1.923)1920 51 1.956 " 1913 3 (1.927)Mar. 1917 95 (1.954) Mar. 1912 5 (1.929)1920 72 1.945 " 1913 o (1.923)Mean 75.2 1.955 Mean 2.^ 1.913Values in parentheses are derived from sun-spot data and are taken from Abbot's curveof equivalent values, Smithsonian Misc. Coll., Vol. 80, No. 2.increased solar activity, whether measured by sun spots, faculae andflocculi, or by an increase in solar radiation reaching the earth.Solar radiation values are missing for a number of the spring andwinter months because no observations were made during thesemonths in the earlier years. These months are included because it
1 A group of solar changes, Smithsonian, Misc. Coll., Vol. 80, No. 2, p. 8, 1927.
8 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 82
was desirable to have an equal distribution of the observationsthroughout the months in order to study and to eliminate seasonalinfluences. If, however, only those months had been used in whichboth values were present, the main conclusions which follow would
Table 3.
—
Mean Departures of Pressure from Normal in Millibars with HighSolar ActivityWinter Half-Year
NO. 7 THE ATMOSPHERE AND THE SUN CLAYTON 9land stations, a further selection was made by grouping the stationsinto areas of 20 of longitude and io° of latitude and taking meansfor each group. Finally, the means for the different groups wereobtained for each io° of latitude. The average departures of theTable 4.
—
Mean Departures of Pressure from Normal in Millibars with Low
IO SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 82
sure from 40 to 70°N., and a defect in the vicinity of the pole, whilethe opposite signs are found in the same latitudes during low solaractivity. MEAN MONTHLY DEPARTURES FROM NORMAL PRESSURE WITH HIGH ANDWITH LOW SOLAR RADIATION.
no. 7 THE ATMOSPHERE AND THE SUN CLAYTON II
tribution of pressure with latitude is shown by a continuous line.The dotted line shows the distribution with high solar activity. Withhigh solar activity the equatorial low pressure belt and the high pres-sure belts in middle latitudes are both intensified and the polaranticyclone diminished. This clearly means an intensification of the
Fig. 7.—Differences in pressure with change from low to high solar activity.Shaded area shows increased pressure, unshaded areas decreased pressure.(Difference between yearly means in tables 3 and 4.)
normal atmospheric circulation. The decrease in the polar anticy-clone is attributed to the increased circulation around the pole, thecentrifugal action developed in the circulating winds causing a fall ofpressure in the polar basin. The effect of the earth's rotation on thewind increases with latitude, and for this reason the fall of pressurein the equatorial belt is greater at latitude 20 than at the Equator.(See fig. 5.) The broken line shows the distribution of pressure with
12 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 82low solar activity. The opposite conditions are here found ; the pres-sure is higher in the tropics and near the pole, and lower in middlelatitudes than the normal pressure.Another fact to be noted is that the maximum of pressure between30 and 40 latitude and the minimum of pressure between 6o° and70 ° latitude are nearer the pole when solar activity is high than whensolar activity is low. This same condition prevails in both the north-ern and southern hemispheres.The changes of pressure due to a change from low to high solaractivity are shown in figure 7, where the changes for each 20 oflongitude and 10 of latitude are plotted on a chart of the northernhemisphere with a polar projection. This map shows a decreased pres-sure all around the world in latitudes of o° to 30 with increased solaractivity. It shows increased pressure between latitudes 40 to 6o°and diminished pressure in the polar basin. But there is evidentlya longitude effect also. The excess of pressure in latitudes 40 toyo° is greatest over the Eurasian continent and least over the PacificOcean.If the values in tables 3 and 4 are corrected for latitude effect bysubtracting the mean values in the last column of the tables, thereis seen to be a distinct tendency for the pressure in all latitudes tobe low over the Pacific and high over Eurasia, with increased solaractivity. Subtracting the yearly means in table 4 from those in table 3and correcting for the latitude effect, the data were obtained fromwhich figure 8 was drawn. The tabulated results are shown intable 5.Table 5.
—
Longitude Differences. Differences in Millibars between the YearlyMeans in Tables 3 and 4 Corrected for Latitude
no. 7 THE ATMOSPHERE AND THE SUN CLAYTON 13tudes over the North Pacific. This longitude distribution is appar-ently another effect of centrifugal action developed by increasedatmospheric circulation with increased solar activity. In regionswhere the air flows more freely, as over the great expanse of thePacific, the centrifugal force developed tends to lower the pressure,especially in high latitudes, more over the water surfaces than overthe land areas.
Fig. 8.—Longitude differences between high and low solar activity.The primary cause of the general atmospheric circulation is be-lieved to be the contrast in temperature between equator and pole.This circulation and all its attendant phenomena changes in unisonwith changes in the amount of solar radiation received by the earth,just as the regulator on a steam engine varies with the amount ofheat received by the boiler.Once in operation there are at least four modifying forces ofimportance acting on the general atmospheric circulation :
14 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 82The first of these modifying forces is the earth's rotation. Theeffect of this rotation is to cause a high pressure belt in middle lati-tudes and a diminished pressure in the polar basin, although it can-not entirely destroy the central high pressure at the pole due toincreased cold without stopping the circulation. Hence, any increasein solar radiation should intensify the pressure belt in middle lati-tudes and lower the pressure in the polar basin, and the reverse withdecreased solar radiation. This is exactly what happens.A second modifying force is the change in cloudiness caused byincreased or decreased atmospheric circulation. Clouds and watervapor * have an important influence on incoming and outgoing radia-tion, so that the belts of cloudiness near the Equator and near 6o°of latitude have an important influence on the temperature and pres-sure and thus should aid materially in maintaining the latitude effectsof changes in solar radiation reaching the atmosphere of the earth.A third modifying force is the movement of ocean water underthe influence of wind. An increase in the general circulation shouldcause an increased flow of ocean waters, with all the modifications inweather which such an increase implies.A fourth modifying force is the distribution of land and water.The influence of all these modifying causes can be seen in the lati-tude and seasonal effects, with differences in solar activity.
III. SEASONAL INFLUENCESWhen the influences of solar changes on the pressure are workedout separately for each month of the year for different places, it isfound that the effect is different at different seasons of the year.At continental stations in high latitudes, such as Dawson, the pres-sure increases much more in mid-winter with increased solar radia-tion than at other seasons, and at mid-summer the effect may even bethe reverse of that in mid-winter. Figure 9 shows the annual periodin the effect of increased solar activity at Dawson. At other stationssuch as Stykkisholm in the North Atlantic and Nome in the NorthPacific there is a dominant semi-annual period in the solar influence.(See fig. 9.) The dotted curves in figure 9 are sine curves derivedfrom the first and second terms of the harmonic formula in a
1 Simpson, G. C, Further studies in terrestrial radiation. Mem. Roy. Meteor.Soc., Vol. 3, No. 21, 1928. Manson, M., The evolution of climates, Baltimore,Aid., 1922. Angstrom, A. K., On radiation and climate, Geogr. An., Vol. 7, p. 122,Stockholm, 1925. Brooks, C. E. P., Climate through the ages, p. 138, London,1926. Abbot, C. G., The radiation of the planet earth to space, Smithsonian Misc.Coll., Vol. 82, No. 5, 1929.
no. 7 THE ATMOSPHERE AND THE SUN—CLAYTON 15
1 2-month period. The 6-month period and the annual period in pres-sure were computed in this way for stations all over the northernhemisphere from the data in " World Weather Records " for the
OCT. NOV. DEC. JAN. FEB. MAR. APR. MAY JUN. JUL. AUG. SEP. OCT.
J6
SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 82
It is seen from this map that the latitude effect as pictured in figure 7is increased twice a year when the sun crosses the Equator in Marchand October. At that time the effect of high solar activity on thepressure is accentuated. The decreased pressure at the Equator, theincreased pressure in middle latitudes and the decreased pressure atthe poles are greater than at other times of the year.
Fig. 10.—Excess or defect of pressure at the Equinoxes (March andSeptember) with increased solar activity.On the other hand, when the sun is at the solstices in June andDecember the latitude differences are diminished and effects due tocontrasts between land and water are accentuated. The greatestincrease of pressure with increased solar activity is over the con-tinents in winter and over the oceans in summer. This is an annualchange in contrast to the semi-annual period in latitude effects. Theannual effect is shown in figure II.
NO. / THE ATMOSPHERE AND THK SUN—CLAYTON IJThis chart is derived from the annual period in pressure as com-puted from the data hy harmonic analysis. The areas outlined onthe chart show where the maximum increase of pressure occursat different seasons when solar activity is greater than normal. Inmid-winter the excess of pressure is greatest over the continentsin high latitudes. There is a defect in the same regions in summer.
Fig. ii.—Regions in which highest pressure occurs at different seasonswith increased solar activity. Annual period.In spring the greatest excess occurs over the North Atlantic andNorth Pacific, and there is a defect in autumn. In autumn there isan excess in middle latitudes and a defect in spring.The results both for the semi-annual period and for the annualperiod were checked by an analysis of the data during periods oflow solar radiation which give in general the opposite effect.The shifting in position of maximum effect on the atmosphere inthe annual period is clearly related to surface conditions and may be
l8 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 82
explained by changes in the balance between incoming and outgoingradiation. In summer the land masses in high latitudes absorb solarheat and this absorption increases with increased solar radiation.There is also an increase of cloudiness at that time which should playan important role in determining the effect of increased solar radia-tion on the atmosphere. In autumn an increased atmospheric cir-culation causes an excess of warm water and of cloudiness in theNorth Atlantic and North Pacific with an accompanying diminution ofpressure. The same increase in atmospheric circulation determines anincreased flow of cold water along the north coast of Africa and ofWestern Mexico and thus determines the opposite annual period inthese regions to that in the northern part of the same oceans.The seasonal shifting in the centers of maximum solar action inthe atmosphere are thus plausibly related to changing physical con-ditions in the atmosphere and in the surface conditions of the earth.IV. ATMOSPHERIC WAVESWhen atmospheric changes, whether of pressure, temperature, orwind movement are analyzed into oscillations of different lengthsthey are usually found not to be stationary but to progress frompoint to point. The short oscillations move fastest and the longeroscillations progress more and more slowly with increasing length.They thus have some analogy to ocean waves and are frequentlycalled waves.Meteorological data may be analyzed into longer and shorter oscil-lations by means of smoothing, by means of using changes of suc-cessively greater length, by means of sine curves derived from indi-vidual periods, or by the process of averaging successive periods,using trial periods of different length. These processes are describedand illustrations given in " World Weather." 1The method adopted for the present research was to select fromplotted curves the cases where an oscillation of some particularlength was unusually strong and then to get the average of severalsuccessive oscillations, so as to eliminate oscillations of longer period.This process was repeated successively for each particular oscillationselected, dropping one and adding another later in time. An exampleof the method is shown in table 6 for St. Paul, Minnesota. The datawere obtained from the Washington 8 a. m. weather map.The consecutive means of four successive periods, obtained asshown in table 6 for the months of November and December, 1927,are plotted in figure 12 for a series of stations running from Nome,
'Clayton, H. H., World Weather, p. 114. New York, Macmillan & Co., 1923.
no. 7 THF. ATMOSPHERE AND Till- SUN CLAYTON 19Table 6.—Means of 4 Periods 0} ~ Days Each, St. Paul, MinnesotaObserved pressure, 29.00 + inches Consecutive means of 4 periods,29.00 +- inchesHay 12 345671234567Nov. 4 .68*1.02 1.32 1.24 1. 1 6 1.26 .8611 .66*1.42 1.26 1. 14 .92*1.38 1.28 .88 1. 12 1. 18 .98 .86*1.29 1. 1318 1.30 1.28 .94 .84* .94 1.26 1.02 1.06 1.24 1. 17 .87 .81*1.18 1.2225 .88 .76 1. 18 .70 .42*1.26 1.36 .98 1.20 1. 15 .79 .76*1.12 1.04Dec. 2 1.40 1.48 1.30 .78* .96 .82 1.20 1.02 1. 10 1.22 .94 .89*1.13 1. 149 1.34 1.28 1. 18 .84 .70*1.14 .58 1. 16 1.26 1.26 1. 10 1.05 .93* .9716 .46* .88 1.20 1.46 1.48 1.32 1.40 etc.23 1.46 1.42 1.38 1.32 1.08 .42* .68* Minimum.
Fig. 12.—-7-day pressure wave.
20 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 82
Alaska, southeastward to Key West, Florida, and to Colon, Panama.It is evident from the plot that the maxima and minima occur laterat southern stations, so that at Williston, North Dakota (not shownin fig. 12), the oscillations are opposite in phase to those at Nome;
Fig. 13.—14-day pressure wave.but further southward at Key West they are in the same phase asat Nome, although much diminished in intensity.Figure 13 shows an oscillation of 13.6 days averaged in overlap-ping two-period intervals. The continuous lines were plotted from
NO. / THE ATMOSPHERE AND THE SUN CLAYTON 21
the averages ; sine curves computed from the data hy harmonic analy-sis are shown by Sotted lines. Here, again, it is found that themaxima and minima of the oscillations occur later at the more south-ern stations and the phase is inverted at St. Paul, showing that theprogressive movement is only about one half as rapid as the 7-dayperiod. In other words the ratio, rate of progress divided by lengthof period, is the same for both periods and apparently for all periods,as will be shown later.That atmospheric pressure and temperature may be analysed intowaves or oscillations which move at different speeds inversely pro-portional to their wave length was advanced by me in the monthlyWeather Review, April, 1907, and has been confirmed by a num-ber of research workers, Defant, Vercelli, Danilow, 1 Clough, 2 Weick-mann,3 and others. These waves do not always move from the samedirection, as Danilow and Weickmann have pointed out ; but thedominant direction of motion is from northwest to southeast in thenorthern hemisphere and from southwest to northeast in the south-ern hemisphere. 4The rate of progress for all classes of moving atmospheric wavesappears to follow a very simple law. This may be illustrated by theprogress of the 7-day wave. Using the data from about 16 sta-tions, the progress of the wave from Alaska is illustrated in figure 14by a series of heavy lines giving the wave front on successive daysas it passed across the North American Continent. Small circles showthe positions of the stations used. It is seen that the wave movedfrom about 180 W. longitude at a rate which would carry it halfaround the world in one period of oscillation, namely in seven days,and hence entirely around in two periods. At the same time thewave front advanced from the Arctic Circle near Nome to the Tropicof Cancer near Key West also in a period of seven days or at a ratewhich would carry it, from pole to Equator in the time of two periodsof oscillation.If, however, the rate of progress is taken not along the wavefront but along a meridian—in this case the 90th meridian west is agood example—the rate of progress southward from the ArcticCircle to the Tropic of Cancer takes place in 3^ days, or at a rate
1 Wetterwellen, Pudoleschen Abtheilung des Ukrainischen MeteorologichesDientes, 1926.2 Monthly Weather Review, Vol. 52, No. 9, p. 436, Sept. 1924.3 Weickmann, L., Das Wellenprobiem der Atmosphare. Meteor. Zeitschr.,S. 241, 1927.4 Clayton, H. H., World Weather, p. in. New York, Macmillan & Co., 1923.
22 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 82
which would carry it from pole to Equator in one period of oscilla-tion. This is evidently a law which applies to wavelike changes ofall lengths.
Fig. 14.—Wave front showing speed of movement in a 7-day wave.
1 Dr. WeickmannV able analysis of the 24-day wave of pres-sure of the winter of 1923-24, it is shown that the wave originated
1 Petermanns Mitteilungen, Erganzungsheft No. 191, 1927.
NO. 7 THE ATMOSPHERE AND THE SUN CLAYTON 2$in the polar basin and spread southward toward the Equator. Fig-ure 15 is derived from a plot made by Dr. Weickmann. The plot ismade to show the wave at successive dates along the meridian of45 E. longitude. The dotted curve No. I in figure 15 shows that onDecember 10 there was a minimum of pressure in the arctic basinnorth of Spitzbergen and a high pressure over Central Asia about6o° N. Six days later, on December 16, as shown by the brokencurve No. 2, the low pressure was about 70 N. and a high pres-sure about 45 N. Twelve days later on December 22, as shownby the continuous curve No. 3, the period was in opposite phase and
10
-J 1 45°E.
DEC. 10 DEC. 16 DEC.22J9Z3.
Fig. 15.—Pressure departures in 24-day period (data derived from diagramby Weickmann).the low pressure is found at 6o° N. with a high pressure southof 30 latitude and also' in the polar basin. Eighteen days later, onDecember 28, as shown by the dotted curve, No. 4, the low pres-sure is at 45 and a high pressure is advancing southward.The plot brings out clearly the decrease in amplitude of the oscil-lations with decreasing latitude. Owing to the decrease of ampli-tude with latitude the velocity of progress of the wave is bestobtained from the points where the curve crosses the zero line.The first zero point is at 72 ° latitude and the second about 30latitude. This is the distance traversed by the wave in 12 days, arate which would carry it from pole to Equator in about one periodof 24 days.In Mr. dough's ' study of a period of about 2.\ years in pres-sure he says : " The epochs of the short period for St. Paul, St. Louis,
'Monthly Weather Review, Vol. 52, No. 9, p. 436, Sept., 1924.
24 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 82Memphis, Vicksburg and New Orleans have been derived and it isfound that there is an average lag of 0.19 year from St. Paul toSt. Louis and a lag of 0.37 year between St. Paul and New Orleans."The distance from St. Paul to New Orleans is 15° of latitude and0.37 year is about one-sixth of the period, so that the rate of prog-
1885 1890 1895 1900 1905 1910
NO. 7 THE ATMOSPHERE AND THE Sl T X—CLAYTON 25
averages. The letters a, 1>, e, etc., show successive maxima. The datawere derived from " World Weather Records " and cover the con-tinent of Asia where the data are more complete for different lati-tudes than in North America.It is seen from the plot that the maxima and minima of the periodoccur first in high latitudes and successively later at stations nearerthe Equator, at least down to ahout 30 latitude, taking ahout threeyears to move from Obdorsk, 66° N., 66° E., to Ley, 34 N., yy° E.In the equatorial belt between 20° N. and 20 S. the maxima andminima occur simultaneously at all stations as shown by the results forMadras and Batavia. However, from figure 16 it is seen that thepressures at Alma Ata, 43 ° N., and at Batavia, near the Equator, areopposite in phase, which is further evidence that this wave traversed90 of latitude in one period of about 3.75 years.A recent study of 2- and 3^-year waves in temperature by ErnestRietschel ' shows a rather complex movement indicating a combina-tion of standing and moving waves.That the law of wave progress quoted above holds true in theSouthern Hemisphere as well as in the northern is shown by therate of progress of a temperature wave of about 18 days shownplotted on page 223 of " World Weather." " This wave progressedfrom Santa Cruz, 50 S., to Cuyaba, 16 S., in seven days, a ratewhich would carry it from pole to Equator along a meridian in oneperiod of 18 days.The rate of progress of a 7.5-year wave is indicated in figure 22where the maxima and minima of the waves occur successively laterat Stykkisholm, Rome, and Calcutta, the minima and maxima atCalcutta being about 7 years later than at Stykkisholm.These facts render it evident that the rate of latitude displace-ment is a general law for periodic oscillations of all lengths. Thislaw may be stated as follows
:
Lazv of latitude displacement of periodic zvaves.—Periodic oscil-lations in atmospheric conditions progress in latitude from point topoint along a meridian at a rate that would carry the wave frompole to Equator in one period, whatever the period of oscillation.It is probable that the law of displacement in longitude is equallysimple. Figure 14 shows that the 7-day wave progressed in longi-tude about 180 , or half around the world, in seven days.
1 Die $-$}, jahrige und die 2 jahrige Temperaturschwankung, von ErnstRietschel. Geographical Institute of the University of Leipzig, Vol. IV, No. 1,1929.
26 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 82
NO. 7 THE ATMOSPHERE AND THE SUN CLAYTON 27A proportional rate of progress appears to occur in the periodicwave of about 7.5 years. Figure 17 shows the centers of oscillation ina 7.5-year wave on a world map. This map is derived from har-monic values computed from groups of three periods between 1883and 1913 at 117 stations scattered over the world. It shows thecenters of oscillations at the epochs, 1885, 1893, 1900, etc. Con-tinuous lines show equal values above normal and broken lines showequal values below normal. It is not possible with available datato follow the progressive movement of all the centers, but the centerover Greenland shows a distinct progress from west to east. Thisprogress will be evident from figure 18 which shows the centers ofoscillation in the area between 50 W. and 120 E. north of the Equa-tor when the epochs are taken successively two years later. Theresults in figure 18 are derived from the data of 48 stations takenfrom " World Weather Records."In 1885 there was a marked excess of pressure over Greenland(see fig. 17) ; in 1887 this center of excess pressure is displaced toNorway; in 1889 this center is over the northern part of centralSiberia; two years later, in 1891, it is over the northern part ofwestern Siberia. The progress of the centers is shown by small cir-cles in the upper chart of figure 18. The circles show that the centerwas displaced eastward about 180 in a period of 7.5 years or at arate which would carry it around the world in two oscillations ofthis period.In his study of the 2|-year period Mr. Clough 1 found that theepochs at Portland, Oregon, preceded those at Toronto by about0.75 year. The difference in longitude is 43 °. At that rate the epochwould move about 150 of longitude in one period, or approximatelyaround the world in two periods.The charts given by Dr. Weickmann in his study of the 24-dayperiod referred to previously do not show the drift in longitude soclearly as the drift in latitude. However, in his charts there arefound centers of maximum departure which show a drift in longi-tude. A center in the Aleutian Islands on December 10, 1923, movedeastward across Canada to Labrador in 1 1 days, which is at the rateof about one period for 180 of longitude; but a center near Green-land moved eastward to northern Siberia and then retreated.The longitude drift of the waves is, hence, not so clearly definedas the latitude drift ; but there is undoubtedly a trend which may bestated as follows
:
1 Monthly Weather Review, Vol. 52, No. 1, p. 30, Jan., 1024.
28 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 82
Fig. 18.—Departures of pressure in 7.5-year period, epochs 1!1889, 1891.
NO. J THE ATMOSPHERE AND THE SUN CLAYTON 29Law of longitude displacement of periodic waves.—-Periodic wavestend to drift eastward at a rate of 180 of longitude in one period,whatever the length of the period. The centers of greatest departureare found in high latitudes, 6o° to 8o° from the Equator.There are several factors which make this drift toward the eastdifficult to follow. First there are the factors depending on solarchanges described in the latitude effect and which are nearly instan-taneous with solar changes. There are also seasonal factors andprobably others which influence the results.Examining the successive charts in figure 18 it is found that themagnitude of the departures in the 7.5-year period decreased rap-idly as the central areas passed into Siberia and increased againover Kamchatka. This enhanced intensity in the departures coincidedwith a maximum of solar activity as will be seen later.Another disturbing factor is the formation of centers of distur-bance moving at right angles to 1 the normal waves. When waves ofhigh pressure and low temperature are advancing from the north-west, low pressure areas form in front of them and advance fromsouthwest to northeast. These disturbances advancing toward thenortheast are particularly frequent over the warm ocean waters tothe east of Asia and of North America. These cross currents greatlycomplicate the normal movement of atmospheric waves and makeanalysis of the data difficult.
V. RELATION OF THE WEATHER WAVES TO SOLAR CHANGESIf the values of solar radiation observed by the SmithsonianAstrophysical Observatory simultaneously with the pressure wavesare treated in the manner just described they show in each casewavelike changes of the same length as the pressure waves.Figure 19 shows the successive means of four periods of sevendays in solar radiation during November and December, 1927, com-pared with the atmospheric pressure observed at the same time atEagle, Alaska, and treated in the same manner as in table 6. Thedotted curves in each case show the harmonic values of the 7-daywave computed from the data. Compare this diagram with the plotsin figure 12.Figure 20 shows the means of successive values of a period of 13.6days in solar radiation and in pressure derived from the means oftwo periods. This diagram may be compared with the plots in fig-ure 13. The dotted curves in figure 20 show harmonic curves com-puted from the data.
3Q SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 82
Fig. 19.—7-day period in solar radiation and pressure.
Fig. 20.— 13.6-day period in solar radiation and pressure.
no. 7 THE ATMOSPHERE AND THE SUN CLAYTON 31Figure 21 shows the observed values of solar radiation duringDecember, 1923, and January and February, 1924. These values arecompared with the observed values of pressure at Spitzbergen andat Hamburg. A 24-day period of oscillation is evident in each caseand this oscillation is shown by the dotted curves computed fromthe data in each case by harmonic analysis. Pressure data from all
Fig. 21.—24-day period in solar radiation and pressure.
over the northern hemisphere were treated in this way for a periodof 24 days by Dr. Weickmann and showed a systematic wavemovement from the polar basin southward.For the study of long periods, no values of solar radiation are avail-able; but the 7.5-year period shows a distinct relation to sun-spotchanges. Figure 22 shows a plot of consecutive means of threeperiods of 7.5 years. This period is one-third of Hale's sun-spotperiod of 22.5 years, and the mean of the three periods eliminatesthe 11.3-year sun-spot period which is one-half of Hale's period.
32 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 82Pressure curves are plotted for five widely separated stations. Theseplots show distinctly an oscillation in the atmosphere of the length of7.5 years and a progress southward from high latitudes.
Fig. 22.—7.54-year period in sun spots and pressure means of 3 periods.VI. SOLAR CYCLES AND WEATHER CYCLESFrom the preceding investigation it is evident that atmosphericand solar conditions show wavelike changes of a periodic nature.The question has long been a challenge to investigators, as to whetherthere are fixed and regular cycles in weather and in solar changes.If such regular cycles could be found, it would greatly assist inunraveling the complexities of the weather and in forecasting futureoccurrences. There is a dominating period of about 11 years in sun-spot numbers, and many efforts have been made to find this same
NO. 7 THE ATMOSPHERE AND THE SUN CLAYTON 33dominating period in weather changes. Such a relation has not beenfound and the reason appears to be that weather changes followchanges in solar radiation more closely than they do sun-spot num-bers, and solar radiation is more variable and shows a more complexperiodicity than do sun spots.When the n-year period 1917 to 1928 is analysed harmonicallyfor sun spots and solar radiation, the results in table 7 are obtained.Table 7.
—
Harmonic Terms for 11%-Year Period in Sun Spots and SolarRadiationSun-spot
34 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 82pressure decreases. This fact is also made very apparent by com-paring the individual periods in sun spots with pressure from 1870to 1920. It is also evident that the amplitude a* of the 11-year periodis not dominant as in the sun-spot period ; but as in the case of solarradiation the subharmonic terms a 2 , az , and a4 , are almost as large asthe primary a x .In order to compare the harmonic terms of the 11^-year period inpressure in equatorial regions with those in other latitudes, the meanpressure was obtained for each io° of latitude in the northern hemis-phere for each year from 1890 to 1913. A period of 23 years wastaken because from Hale's observations of magnetism in sun spotsthe complete period of the sun spots is about 22.6, so that 11.3years becomes the second harmonic of this period. From the datathus obtained harmonic terms were computed for each zone of lati-tude and are given in table 9. The phases of the periods varied forTable 9.
—
Amplitudes of the Harmonics of a 22.6-Year Period in Pressure
NO. 7 THE ATMOSPHERE AND THE SUN CLAYTON 35periods besides the n-year period. Turner found evidences of aperiod of 260-280 years from a study of tree rings, Nile floods, Chi-nese earthquakes, and sun spots. (Mon. Not. Roy. Astron. Soc, 1919and 1920.) According to a recent analysis of the Wolfer sun-spotdata made by Dinsmore Alter, published in the Monthly WeatherReview of October, 1928, there are solar periods of more than 200years in length, and the 11-year sun-spot period is a subharmonic ofmuch longer periods. This view agrees with that put forward byEllsworth Huntington and S. S. Visher in " Climatic Changes,"1922, p. 45. My own investigations are in accord with this view, ex-cept that recently the longer periods seems somewhat greater than thatgiven by Alter.Beginning with a period of 90 years, instead of 84 as given byAlter, I find periods of approximately the following length: Lengthof solar periods in years: 90, 56, 45, 35, 30, 28, 22.5, 18, 15, 12.9,11^, 10, 9, 8.2, 7^, etc. All of these shorter periods are subharmonicsof 90 years, except 56, 35, and 28, which are harmonics of a longerperiod.They agree very well with meteorological cycles found by Prof.A. E. Douglass * from rings indicating the annual growth of trees inthe southwestern part of the United States where rainfall is the mostessential factor in growth. The periods found by Professor Douglassare: 35> 3 1 . 28, 22.5-24.0, 20.5, 17.2, 14.2, 1 1.2-1 1.7, 10.2, 8.6, 7.6, 6.8years.A study of periodicities in the Nile floods by C. E. P. Brooks 2leads him to pick out the following periods in years : 76.8, 64.6-67.4,39-85> 3349. 24.43, 21.81-22.43, 18.32, 16.68, 14.87, 12.50, 10.86-11.36, 8.33, 7.33, 6.83, 5.52, 3.66, 2.86. It is pointed out that 11 outof 16 of these periods are multiples or submultiples of a period of22.12 years. This period is somewhat shorter than Hale's period of22.6 years ; but the difference may be due to- the fact that the periodactually was shorter during the intervals covered by Brook's datawhich go back to the year 641. His data indicate a systematic varia-tion in the phase of this period, so that at the end of about 200years the phase is inverted as regards epochs 200 years earlier.The researches of D. Brunt 3 also indicate that there are a greatmany meteorological cycles, or else there are none. Plis periods inyears derived from the Greenwich temperatures are : 2^, 17.5, 15, 8.17,
1 Climatic cycles and tree growth, Vol. 2, p. 123. Carnegie Inst, of Washington,1928.2 Mem. Roy. Meteorol. Soc, Vol. II, No. 12, 1928.3 Quart. Journ. Roy. Meteorol. Soc, Vol. 53, No. 221, Jan., 1927.
36 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 82
7.34; and in months, 64, 60, 42, 37, 26, 25, 21 J, 19.3-19.5, 14.5-14.7, 13, 12J. The researches of Dinsmore Alter * published in theMonthly Weather Review also bear testimony to the multiplicity ofmeteorological cycles.My own researches have dealt largely with shorter periods of daysand months rather than years, principally because there was a muchlarger mass of data available for discussion. In my earlier studiesof pressure and temperature data in the United States. 2 I found thefollowing periods in days: 3, 3.6, 4.6, 5.45, 6.14, 7.24, 9.1, 11, 18, 22,29, 44, 58, etc. My recent studies indicate that there are many morecycles and that all are probably harmonics of the sun-spot cycle.A. Defant 3 in a world-wide study in 1912 found the followingperiods in days: 4.4, 7.9-8.7, 12.0-13.0, 16.8, 24.5, 31.2-31.5. Arc-towski, Turner, Simpson, Wallen, Myrback, Wasserfall, Schosta-kowitsch, and Kidson have all found short meteorological cycles ofvarious lengths Even the short period cycles of a few days areprobably submultiples of much longer solar cycles, the most promi-nent of which is the 11-year sun-spot cycle, or its double value, the22.5-year cycle.In most cycles the subharmonics of small length are not important,but it has been shown in table 9 that in high latitudes the subhar-monics of the 1 1 -year period in meteorological cycles are of greateramplitude than the primary period of 11 years and that the ampli-tude increases with decreasing length of the harmonic. The sequencehas not been followed through for the entire Northern Hemispherebeyond the period of about four months, but the amplitudes ofmeteorological cycles at stations in the northern United States andCanada apparently increase down to a length of about three days.These shorter periods determine the origin and movement of theordinary cyclones and anticyclones seen on the weather map.Most investigators of meteorological cycles assume at the begin-ning of their work that any cycle which may exist is constant inamplitude and phase and may by repetition be separated from otherchanges by which it is masked. This belief is the basic assumptionunderlying the analysis by the Fourier series or the Schuster peri-odogram. Prolonged investigation usually convinces the researchworker that this assumption cannot be maintained. I early became
1 Monthly Weather Review, Vol. 54, p. 44, and Vol. 55, pp. 60 and 263.2 Amer. Meteorol. Journ., Feb., 1895, p. 376 ; also Amer. Journ. Sci., March,1894.3 Sitzungberichte d. Wiener Akad., Bd. 121, Heft 3.
no. 7 THE ATMOSPHERE AND THE SUN CLAYTON
convinced that meteorological cycles change hoth in amplitude andphase. (Science, 1898, p. 243.)Figure 23 shows an analysis of the Wolfer sun-spot numbersbetween 1890 and 1913 into a period of 22.6 years and its harmonics.It is seen that the chief period is one of 11.3 years, but some of theother periods show a fairly large amplitude of oscillation.
1890 1895 1900 1905 1910
38 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 82Certain common features stand out clearly in all these charts.First, in the equatorial belt, except possibly over parts of the PacificOcean, the pressure is lower than normal at the time of maximum
Fig. 24— 11.3-year period in pressure = \ of 22.6 years. Departures at timeof maximum of solar period of same length.
solar activity in each period. Second, in middle latitudes of theSouthern Hemisphere there is a tendency to a belt of pressure abovenormal which cannot be well outlined on account of insufficient
Fig. 25.—5.65-period in pressure = \ of 22.6 years. Departures at timeof maximum of solar period of same length.
observations. Third, in the Northern Hemisphere in high latitudesthere is a tendency for the departures to form centers of positive andnegative departures, usually two centers of positive departure, and
no. 7 THE ATMOSPHERE AND THE SUN—CLAYTON 39two centers of negative departure. Fourth, these centers are not inthe same geographical position for the different periods and do notremain fixed for successive epochs of the same period. The reasons
Fig. 26.—3.77-year period in pressure = i of 22.6 years. Departures at timeof maxima of solar period of same length.for these shifting centers are not clear. They are associated withchanges in the phase and amplitude of the cycles.Changes in amplitude are both apparent and real. Apparentchanges occur where two periods of nearly the same length first
Fig. 27.—2.82-year period in pressure = | of 22.6 years. Departures at timeof maxima of solar period of same length.
strengthen each other when they are in the same phase and thenweaken each other when they are opposed in phase. This change willbe familiar to most readers from diagrams to illustrate beats in sound
40 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 82
waves. The beats are even more complicated when there are three ormore periods of nearly the same length. In such a case there may bean apparent change of phase in one of the periods.Real changes in amplitude are brought about by the influence oflonger periods on shorter periods. An example of this is the influ-ence of the annual period on shorter weather cycles. All weatherchanges are most intense in winter, because then the contrasts intemperature between Equator and pole, between ocean and continent,and between adjacent bodies of land and water are at a maximumintensity and the general atmospheric circulation is increased.Also all periodic changes in the atmosphere are more intense whensolar activity increases. The reason for this increased intensity willbe clear, first from the fact shown in the early part of this paperthat increased contrasts of temperature and pressure in the atmos-phere result from increased solar activity, and second from the factthat the amplitude of the solar cycles increases with increased solaractivity.An example of the increased amplitude of solar periods withincreased solar activity is shown in figure 22 where the amplitudes ofthe 7.5-year sun-spot period is distinctly greater during the inter-val 1865 to 1875, when the general level of solar activity was higher,than during the interval 1885 to 1895, when it was lower. Theincrease of amplitude during the first of these intervals and decreaseduring the second was also evident in the sun-spot cycle and in itsharmonics of 5.65, 3.75, 2.82 years, etc.An example of increased amplitude of meteorological cycles withincreased solar activity is shown in figure 28 where a period of 7^months in pressure at Chicago shows a marked increase in ampli-tude at the time of maximum of sun spots in 191 7 and a diminishedamplitude during the intervals of minima of sun spots in 19 13 and1 923- 1 924. The data for this curve are the means of 10 overlappingperiods of j\ months obtained in the manner indicated in table 6.The dotted curves are sine values computed for each individualperiod.That meteorological cycles change in phase as well as in intensityis also evident. These changes of phase appear to arise from severaldifferent causes. First, the solar periods themselves change phase. Inmost cases this change occurs suddenly and appears to be about 180
i
NO. / THE ATMOSPHERE AND THE SUN CLAYTON 41
U
42 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 82
or a complete reversal in phase. Figure 29 shows what appears to bea reversal in phase in the sun-spot cycle. The average length of thiscycle is about 11 years, so that two cycles occur in 22.5 years. If thecycles are plotted in 22-year periods as in figure 29 it is seen that inthe period 1770 to 1792 the cycle is nearly inverted in phase to thecycles occurring 22 years earlier and 22 years later. It is, however,quite possible that this result is due either to interference of periodsof different lengths, or to> lack of accuracy in the early observations.No such apparent inversion has occurred since 1800.
YEAR 1 2 3 4 5 6 7 8 9 10 II 12 13 14 15 16 17 18 19 20 21 22
no. 7 THE ATMOSPHERE AND THE SUN CLAYTON 43
of pressure, when it rises in one part of the world, there is an equiva-lent fall in other parts. These centers of rise and fall are not fixedin position, hut shift their position to 1 some extent as illustrated inthe case of a 25-month period in a preceding paper of this series.1The variations in intensity and phase of solar and meteorologicalcycles makes the investigations of the separate cycles difficult. Theuse of the Fourier series and of the Schuster periodogram are notwell adapted to such work. In order to meet these difficulties Idevised the correlation periodogram ' which is to a considerableextent independent of variations in intensity of the periods ; butdoes not overcome the difficulty of shifting of phase. The best
YEAR 1 2 3 4 5 6 7 8 9 10 II 12 13 14 15 16 17 Id 19 20 21 22
44 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 82
VII. THE USE OF WEATHER CYCLES IN FORECASTINGHaving' developed methods of separating and studying variousconditions which make up the weather, it seemed important that atest be made of the possibility of using them in practical forecasting.Forecasting future weather conditions in the present state of knowl-edge may be undertaken in at least three different ways : ( I ) Bytracing out the results which follow the increase or decrease in thegeneral circulation of the air with changes in solar activity. (2)By analyzing and following weather waves of different classes. (3)By computing the amplitudes and phases of different cycles foundin solar and weather changes and projecting these forward into thefuture.In regard to the use of the first method, since increased solaractivity is attended by a fall of pressure in equatorial regions andby increased contrasts of pressure in higher latitudes, there is broughtabout an increased atmospheric circulation and certain general con-ditions follow
:
( 1 ) The cloudy and clear belts of the world are intensified andthus alter the incoming and outgoing radiation.(2) The increased air circulation means an increased flow of oceanwaters which brings an increased northward flow of warm wateralong the east coast of the United States and Japan and an accumula-tion of warmer water in the North Atlantic and North Pacific. Theaccumulation of warmer waters in these regions especially in autumnbrings increased cloudiness and increased rainfall. The increasedcloudiness reacts by diminishing radiation losses from the earth andthus further modifying weather conditions. On the other handthe increased oceanic circulation brings increased cold water to theshores of North Africa and southern California, and produces achain of atmospheric conditions which affect the northern shores ofSouth America and the West Indies and extend well out into thePacific. A parallel set of changes is produced in the Southern Hemis-phere in an opposite way on the east and west sides of the con-tinents. When solar activity diminishes the reverse conditionsprevail.(3) Increased solar activity brings also an increased flow of airover the continents and with it an increased rainfall in certain regionsand a decreased rainfall in other regions. The distribution of pres-sure and attendant conditions is to a large degree influenced by theseasons.
NO. 7 THE ATMOSPHERE AND THE SUN CLAYTON 45Hence, to follow the sequences of weather resulting from increasedsolar activity it is necessary to consider the month or seasons sepa-rately and to work out expected conditions for different intensities ofsolar activity.In regard to the use of the second method, forecasting weather asordinarily practiced at the present time depends on anticipating fora day or two at a time the drift of weather conditions. Such fore-casts can be improved and extended in time by analyzing weather intowaves of different lengths and forecasting the progress of thestronger waves. Even long range forecasts can be made on this basis,as I have demonstrated by actual tests.The third method of forecasting is by means of the periodicvibrations in the sun and atmosphere. Any pulsation in solar condi-tion will be attended by similar pulsations in the earth's atmosphere.The shorter pulsations will be felt relatively more in high latitudesof the earth and the longer pulsations relatively more at low lati-tudes, but all will be repeated to> some extent in every part of theatmosphere. An analysis of the periodic terms in the weather at anypoint on the earth would make it possible to project the periodicterms ahead to> any length of time desired, were there no variationsin the amplitude and phase of the periods. But there are variationsand for this reason it is necessary to redetermine the periodic termsat short intervals and to limit the time in advance which they aremade to cover. When these variations in the periodic terms becomecalculable, this method of forecasting will probably replace all others.Already considerable progress has been made along this line.In practical forecasting at present it is desirable to consider all ofthe three methods mentioned and to use them as checks on eachother. Forecasting in words has but little meaning to the averageexpert, because the meanings of words can be interpreted in varioussenses and there are no accepted rules for verifying such cases.Quantitative forecasts can, however, be verified by accepted stand-ards ; so that from the beginning of my experiments in forecasting,both verbal and quantitative forecasts were made. These quantitativeforecasts were made first for about a week in advance, then forlonger intervals up to a month. Figure 31 gives one of the morerecent of these forecasts of pressure made on November 24, 1929, for27 days in advance beginning on November 26 and ending onDecember 21. The forecast was made up from a combination ofcycles varying in length from 3 days to 13 days. The correlation ofthe forecasted with the observed pressure is 0.64 ±0.06.
46 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 82By computing pressure in this way for a network of stations,weather maps bearing unmistakable resemblance to observed weathermaps may be computed in advance. In March, 1929, values of pres-sure were computed for one week in advance for 23 selected sta-tions forming a net over the United States and from these computedvalues lines of equal pressure departures were drawn. The maps
NOVEMBER, 1929 DECEMBER26 27 28 29 30 1 2 3 4 5 6 7 8 9 10 II 12 13 14 15 16 17 18 19 20 21
NO. THE ATMOSPHERE AND THE SUN CLAYTON 47
MARCH 13 FORECASTED PRESSURE MARCH 13
PRESSURE MARCH 14 FORECASTEC PRESSURE MARCH 14. OBSERVED,
PRESSURE MARCH 15
Fig. 32.—Pressure forecasted from a combination of meteorological cycles.
APRIL MAY JUNE JULY AUGUST
48 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 82
mean a revolution in present methods of weather forecasting. Theforecasting of pressure and temperature will be made in much thesame way that ocean tides are now predicted, except that the periodsused will be solar periods rather than lunar periods and will needto be treated in a special way owing to changes in phase andamplitude.Such a successful forecast as that shown in figure 31 seems con-clusive evidence that day to day weather is not a haphazard occur-rence as many persons believe, but is subject to calculation. It isevident that changes of pressure are calculable to some extent now,and the calculations will, no doubt, in the future be made withincreasing accuracy for weeks and perhaps months in advance. Proc-esses will be simplified and machinery like the tidal machines will beintroduced in order to handle the immense amount of data which willbe needed for world-wide forecasts, or even for forecasts over a largearea like the United States. SUMMARYThis paper contains evidence pointing to the following conclusions
:
Solar activity varies in complicated pulses. These pulses or varia-tions in intensity are attended by variations of pressure in the earth'satmosphere. When solar activity, as indicated by spots and radia-tion values, increases, the latitude contrasts of pressure in the earth'satmosphere are increased and atmospheric circulation speeded up.The pressure falls in the equatorial belt, rises in middle latitudesand falls in the polar regions. When solar activity decreases thereverse conditions occur. The zonal regularity of these changes isinterfered with by the distribution of land and water and by seasonalchanges.Immediately following the decrease of pressure in the polar regionwith increased solar activity, a wave of decreased pressure movestoward the Equator. With decreased solar activity the pressure inpolar latitudes increases and a wave of increased pressure travelstowards the Equator. These waves move with a speed proportional tothe length of the solar pulse or period causing them. If the period ofoscillation is seven days the wave moves from pole to Equator, whenmeasured along a meridian, in seven days. If the length of theoscillation is 2.°/ months, or 2.\ years, the time of the wave movementfrom pole to Equator is 27 months and if the length of the period is7^ years the time of movement from pole to Equator is j\ years, orone period of oscillation in each case.
NO. / THE ATMOSPHERE AND THE SUN CLAYTON 49There are also east to west movements of the waves, and thereare probably returning waves toward the poles of less intensity ; sothat the observed phenomena are extremely complex. The analyzedwave movements are subject however to apparently simple laws, andcan, therefore, probably be computed and combined to produce ob-served conditions.The observed data of sun-spot numbers and solar radiation valueswhen subjected to harmonic analysis for the n-year period 1917 to1928 show that the dominating period of about 11 years in sunspots is no more marked in solar radiation values than the subhar-monics of h j, }, etc., of the 11-year period which have ampli-tudes nearly as large as the n-year period itself.When the pressure observations in the Tropics are subjected toharmonic analysis they show periods resembling in amplitude thoseof solar radiation values and not those of sun spots. The analyses ofthe data in higher latitudes show that the amplitudes of the subhar-monics increase with latitude, so that in high latitudes in the neigh-borhood of the pole the subharmonics become vastly more importantthan the primary period.A study of the possibility of analyzing the data at each particularpart of the earth with the view to discovering fixed periodic cyclesindicates that if such cycles exist, the amplitudes are subject towide variations and even to inversion of phase from time to time.However, when the complex cycles are analyzed individually andaverages taken for a small number of successive cycles, it is possibleto project them into the future and combine and plot them in a curvewhich at times has a striking resemblance to observed data. As knowl-edge of methods and laws of change progress, this kind of fore-casting will undoubtedly be done with increasing accuracy.